How do you find the domain and range of #y = sin(2x)#?

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Answer 1 · 2017-10-25T11:06:24

Domain: #(-oo, +oo)#
Range: #[-1, +1]#

#y=sin(2x)#

#y# is defined #forall x in RR#

#:.# the domain of #y# is #(-oo, +oo)#

Let #theta = 2x#

#y = sin theta -> -1<= y <= +1 forall theta in RR#

Hence, #y = sin(2x) -> -1<= y <= +1 forall theta in RR#

#:.# the range of #y# is #[-1, +1]#

We can observe the domain and range of #y# from the graph of #y=sin(2x) below.

graph{sin(2x) [-6.25, 6.234, -3.12, 3.124]}

Answer 2 · 2017-10-25T11:10:49

Domain: # -oo < x < oo or x| (-oo ,oo)#
Range: #−1 ≤ y≤ 1 or [-1.1]#

#y=sin(2x)# , the domain of the function y=sin(2x) is all real

numbers (sine is defined for any angle measure),

i.e # -oo < x < oo or x| (-oo ,oo)#

The range is #−1 ≤ y≤ 1 or [-1.1]# , as maximum and minimum

value of #y# lie in between #-1# and #1# , inclusive.

Domain: # -oo < x < oo or x| (-oo ,oo)#

Range: #−1 ≤ y≤ 1 or [-1.1]#

graph{sin(2x) [-10, 10, -5, 5]} [Ans]